I have also been trying to get serial ports working on my system. To start with, create symlinks in your .wine/dosdevices directory that point to your serial ports. If you don't do this, wine will default to com1 -> /dev/ttyS0
in your case,
cd ~/.wine/dosdevices
ln -s /dev/ttyR0 com1
ln -s /dev/ttyR1 com2
etc....
Then you must ensure your linux user has permission to access the serial ports. On my system (Ubuntu 8) I added my user to the 'dialup' group.
Unfortunately, I can send data out the serial port, but not receive it properly.